Answer
The limit does not exist.
Work Step by Step
As we can see from the attached graph, as $x$ gets closer and closer to $1$ from the left, the value of the function (the $y$-value) gets closer and closer to $3$. But, as we can see, as $x$ gets closer and closer to $1$ from the right, the value of the function (the $y$-value) gets closer and closer to $2$. Thus the limits from the two sides differ and the overall limit does not exist.
